if we want to study a parabola: y = (x)^2 ; such that the vertex is x = 5, y=3 it is better to study this when the vertex is at the origin so we move it by -5, -3 to get it to (0,0)
y-3 = (x-5)^2
y = (x-5)^2 + 3

now consider the equation
y-d=a sin (b(x+c))
this means that all the points with y-coordinate y has now the y coordinate of y-d
this is a vertical shift of the entire function
if d is positive, the entire function shifts down by d units
and if d is negative the entire function shifts up by d units

a is a scalar factor that affects the slope of this thing at any given point.
if we take the sine wave, it only has values from -1 to 1, the "a" part manipulates the slope at every given point to change how high or low the sin function can reach